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MHD equilibrium: Difference between revisions
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The force balance equation also implies that the surface ''p'' = constant is a flux surface (assuming flux surfaces exist). | The force balance equation also implies that the surface ''p'' = constant is a flux surface (assuming flux surfaces exist). | ||
In three dimensions (as opposed to the ''effectively'' two-dimensional axisymmetric situation), the existence of flux surfaces (nested or not) is not guaranteed. | In three dimensions (as opposed to the ''effectively'' two-dimensional [[axisymmetry|axisymmetric]] situation), the existence of flux surfaces (nested or not) is not guaranteed. | ||
<ref>[http://dx.doi.org/10.1063/1.1761965 H. Grad, ''Toroidal Containment of a Plasma'', Phys. Fluids '''10''' (1967) 137]</ref> | <ref>[http://dx.doi.org/10.1063/1.1761965 H. Grad, ''Toroidal Containment of a Plasma'', Phys. Fluids '''10''' (1967) 137]</ref> | ||
Assuming an initial situation with nested magnetic surfaces, the [[Rotational transform|rotational transform]] of the field line on the surface may either be irrational so that the field line covers the surface entirely (ergodically), or rational. | Assuming an initial situation with nested magnetic surfaces, the [[Rotational transform|rotational transform]] of the field line on the surface may either be irrational so that the field line covers the surface entirely (ergodically), or rational. | ||
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== Numerical codes == | == Numerical codes == | ||
In two dimensions (assuming [[ | In two dimensions (assuming [[axisymmetry]]), the force balance equation reduces to the | ||
[[:Wikipedia:Grad-Shafranov equation|Grad-Shafranov equation]]. | [[:Wikipedia:Grad-Shafranov equation|Grad-Shafranov equation]]. | ||
A large number of codes is available to evaluate MHD equilibria. | A large number of codes is available to evaluate MHD equilibria. | ||